Engineering Rock Mechanics

Stress-controlled instabiliv mechanisms 35 1

From these equations we can see that:

(a) when p = p,, the internal pressure replaces the hydrostatic stress field
present in the rock before excavation and then 0, = 00 = p;
(b) considering p as a support pressure in a tunnel, the magnitude of p is
typically very low compared to that of p,, and so has little influence on
either 0, or 00;
(c) by pressurizing the fluid in a borehole, it is possible to produce
conditions where p > pz, and if p > 2pz, then 00 will become negative,
i.e. tensile, and, depending on the tensile strength of the rock,
hydraulic fracturing may occur as shown in Fig. 4.5.

Several special cases have been given here, and by extension the ideas
developed can be considered for more complex situations. One concept
that can be elegantly demonstrated from the Kirsch equations is the
principle of the conservation of load.

Conservation of loud. Figure 19.12 shows, by means of sketches represent-
ing different stages in a hypothetical excavation process, how the distribu-
tion of vertical stress across a horizontal plane changes. The argument can
be used to analyse the stress distribution on any plane-we have chosen
the horizontal plane coincident with the centre of the excavation for the
sake of convenience. Fig. 19.12(a) indicates this cross-section through a
CHILE rock mass, with the future excavation shown as a dotted line, and
the horizontal plane shown as a dashed line. Fig. 19.12@) shows a free body
diagram of the rock above this horizontal plane. In this case, the effect of

n

F = pzA

F = p,A

Areas equal = p,a

Diameter = 2a

Figure 19.12 Principle of conservation of load before and after excavation.